6 March 2011

An
article by Fairfax on the
magnitude 6.3 earthquake that devastated the city of Christchurch in New
Zealand includes an interactive diagram of several earthquakes which are compared
by the relative sizes of circles shown on a map.

The
magnitude 7.9 earthquake that occurred in Sichuan, China on 12 May, 2008,
appears nearly as large as the catastrophic
magnitude 9.1 earthquake near northern Sumatra on 26 December, 2004. It is
not a meaningful comparison, because
earthquake magnitudes are measured on a logarithmic scale. An increase
in magnitude by one unit represents a tenfold increase in the maximum amplitude
of the seismic waves recorded by the seismograph and about 32 times the amount of
energy released. Thus the magnitude 9.1 earthquake near northern Sumatra had an
amplitude 109.1 - 7.9 = 15.8 times larger than the magnitude 7.9 earthquake
in Sichuan, China, and 109.1 - 6.3 = 631 times larger than the magnitude
6.3 earthquake in Christchurch.

According to an empirical
relationship developed by Beno Gutenberg and Charles Richter, log10E
is proportional to 1.5M, where E is the energy released by the earthquake
and M is the magnitude. This means that in terms of energy released, the
magnitude 9.1 earthquake was about 101.5(9.1 - 7.9) = 63.1 times stronger
than the magnitude 7.9 earthquake, and about 101.5(9.1 - 6.3) ≈
15800 times stronger than the magnitude 6.3 earthquake.